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Found 2 items, similar to Circle of curvature.

**English → English** (WordNet)
Definition: circle of curvature
circle of curvature
n : the circle that touches a curve (on the concave side) and
whose radius is the radius of curvature [syn: osculating circle
]

**English → English** (gcide)
Definition: Circle of curvature
Curvature *\Cur"va*ture\* (k?r"v?-t?r; 135), n. [L. curvatura. See
Curvate.]
1. The act of curving, or the state of being bent or curved;
a curving or bending, normal or abnormal, as of a line or
surface from a rectilinear direction; a bend; a curve.
--Cowper.
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The elegant curvature of their fronds. --Darwin.
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2. (Math.) The amount of degree of bending of a mathematical
curve, or the tendency at any point to depart from a
tangent drawn to the curve at that point.
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Aberrancy of curvature (Geom.), the deviation of a curve
from a circular form.
Absolute curvature. See under Absolute.
Angle of curvature (Geom.), one that expresses the amount
of curvature of a curve.
Chord of curvature. See under Chord.
Circle of curvature. See Osculating circle of a curve,
under Circle.
Curvature of the spine (Med.), an abnormal curving of the
spine, especially in a lateral direction.
Radius of curvature, the radius of the circle of curvature,
or osculatory circle, at any point of a curve.
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Circle *\Cir"cle\* (s[~e]r"k'l), n. [OE. cercle, F. cercle, fr. L.
circulus (Whence also AS. circul), dim. of circus circle,
akin to Gr. kri`kos, ki`rkos, circle, ring. Cf. Circus,
Circum-.]
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1. A plane figure, bounded by a single curve line called its
circumference, every part of which is equally distant from
a point within it, called the center.
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2. The line that bounds such a figure; a circumference; a
ring.
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3. (Astron.) An instrument of observation, the graduated limb
of which consists of an entire circle.
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Note: When it is fixed to a wall in an observatory, it is
called a mural circle; when mounted with a telescope
on an axis and in Y's, in the plane of the meridian, a
meridian circle or transit circle; when involving
the principle of reflection, like the sextant, a
reflecting circle; and when that of repeating an
angle several times continuously along the graduated
limb, a repeating circle.
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4. A round body; a sphere; an orb.
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It is he that sitteth upon the circle of the earth.
--Is. xi. 22.
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5. Compass; circuit; inclosure.
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In the circle of this forest. --Shak.
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6. A company assembled, or conceived to assemble, about a
central point of interest, or bound by a common tie; a
class or division of society; a coterie; a set.
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As his name gradually became known, the circle of
his acquaintance widened. --Macaulay.
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7. A circular group of persons; a ring.
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8. A series ending where it begins, and repeating itself.
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Thus in a circle runs the peasant's pain. --Dryden.
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9. (Logic) A form of argument in which two or more unproved
statements are used to prove each other; inconclusive
reasoning.
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That heavy bodies descend by gravity; and, again,
that gravity is a quality whereby a heavy body
descends, is an impertinent circle and teaches
nothing. --Glanvill.
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10. Indirect form of words; circumlocution. [R.]
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Has he given the lie,
In circle, or oblique, or semicircle. --J.
Fletcher.
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11. A territorial division or district.
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Note:
The Circles of the Holy Roman Empire, ten in number, were
those principalities or provinces which had seats in the
German Diet.
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Azimuth circle. See under Azimuth.
Circle of altitude (Astron.), a circle parallel to the
horizon, having its pole in the zenith; an almucantar.
Circle of curvature. See Osculating circle of a curve
(Below).
Circle of declination. See under Declination.
Circle of latitude.
(a) (Astron.) A great circle perpendicular to the plane
of the ecliptic, passing through its poles.
(b) (Spherical Projection) A small circle of the sphere
whose plane is perpendicular to the axis.
Circles of longitude, lesser circles parallel to the
ecliptic, diminishing as they recede from it.
Circle of perpetual apparition, at any given place, the
boundary of that space around the elevated pole, within
which the stars never set. Its distance from the pole is
equal to the latitude of the place.
Circle of perpetual occultation, at any given place, the
boundary of the space around the depressed pole, within
which the stars never rise.
Circle of the sphere, a circle upon the surface of the
sphere, called a great circle when its plane passes
through the center of the sphere; in all other cases, a
small circle.
Diurnal circle. See under Diurnal.
Dress circle, a gallery in a theater, generally the one
containing the prominent and more expensive seats.
Druidical circles (Eng. Antiq.), a popular name for certain
ancient inclosures formed by rude stones circularly
arranged, as at Stonehenge, near Salisbury.
Family circle, a gallery in a theater, usually one
containing inexpensive seats.
Horary circles (Dialing), the lines on dials which show the
hours.
Osculating circle of a curve (Geom.), the circle which
touches the curve at some point in the curve, and close to
the point more nearly coincides with the curve than any
other circle. This circle is used as a measure of the
curvature of the curve at the point, and hence is called
circle of curvature.
Pitch circle. See under Pitch.
Vertical circle, an azimuth circle.
Voltaic circuit or Voltaic circle. See under Circuit.
To square the circle. See under Square.
Syn: Ring; circlet; compass; circuit; inclosure.
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